Method for determining the state of a cell

ABSTRACT

A method for identifying a state of a cell contained in a sample, including: illuminating the sample using a light source by producing an incident light wave propagating toward the sample; then acquiring, using a matrix-array photodetector, an image of the sample, the sample being placed between the light source and the matrix-array photodetector such that the matrix-array photodetector is exposed to a light wave resulting from interference between the incident light wave and a diffraction wave produced by each cell; applying a numerical reconstruction algorithm to the image acquired by the matrix-array photodetector, to estimate a characteristic quantity of the light wave reaching the matrix-array detector, at a plurality of distances from the matrix-array photodetector. The value of the characteristic quantity, or its variation as a function of distance, allows the state of the cell to be determined from among predetermined states.

TECHNICAL FIELD

The invention relates to the field of analysis of cells, and moreprecisely to the inspection of the proliferation of cells, in incubatorsor biological reactors.

PRIOR ART

The inspection of the development of cells in incubators or biologicalreactors is an essential step in the process of producing cells. Inthese applications, the cells are placed in a culture medium, propitiousto their development.

Their number and their state, and in particular whether they are aliveor dead, are regularly inspected. These inspecting operations requirethe use of a microscope, the cells being marked beforehand using afluorescent tag or a chromophore, the level of fluorescence of cellsvarying depending on whether they are alive or dead. Such a method hascertain drawbacks: firstly, it requires the use of a microscope, a pieceof equipment that is costly and bulky. In addition, since the field ofobservation is small, the analysis of a spatially extensive samplerequires time because it is necessary to move the sample in front of themicroscope. Moreover, marking cells with a fluorescent label or achromophore may have consequences on their development.

One of the pursued avenues of research is the use of simple opticalmethods, such as lensless imaging. The observation of biologicalparticles by lensless imaging has seen a certain amount of developmentsince the end of the years 2000. This technique consists in placing asample between a light source and a matrix-array photodetector or imagesensor. The image captured by the photodetector is formed byinterference between the incident wave, produced by the light source,and the wave diffracted by the particles making up the sample. Thisimage is frequently referred to as a “hologram”. Thus, for eachparticle, it is possible to record, on the sensor, a diffraction patternthat is specific thereto. Applied to biological samples, this techniquehas been described in document WO2008090330. It is then possible toperform a simple analysis of each particle, by comparing the diffractionpattern that it generates with diffraction patterns establishedbeforehand and corresponding to known particles. However, this methodmay reach limits as particle concentration increases.

It is possible to apply mathematical techniques i.e. what are referredto as digital holographic reconstruction techniques, in order toconstruct what is called a complex image of each particle present in thesample. This type of technique consists in back-propagating the lightwave to the object plane, in which the particles are located, saidobject plane being located a known distance from the image. Applicationsto the characterization of cells on the basis of a reconstructed compleximage have been described in the documents US2012/0148141 andWO2014/012031, the cells being spermatozoa. However, these methods arelimited to estimation of the properties of said cells, and their path,from the reconstructed complex image. A complex image of a sample may beinsufficient to identify a particle.

Therefore what is sought is a method for observing cells, and inparticular a means for discriminating living and dead cells, which issimple, inexpensive, reliable, does not require cells to be marked andhas an extensive field of observation.

DISCLOSURE OF THE INVENTION

The invention responds to this problem by providing a method fordetermining the state of a cell, said cell being placed in a sample, themethod including the following steps:

-   illuminating said sample using a light source, the light source    producing an incident light wave propagating towards the sample    along a propagation axis;-   acquiring, using a matrix-array photodetector, an image of the    sample, the sample being placed between said light source and said    matrix-array photodetector in such a way that the matrix-array    photodetector is exposed to a light wave comprising interference    between the incident light wave and a diffraction wave produced by    each cell;-   determining a position of said cell in a plane parallel to a    detection plane in which the matrix-array photodetector lies;-   applying a digital reconstruction algorithm to said acquired image,    so as to determine at least one characteristic quantity of the light    wave to which the matrix-array photodetector is exposed, at said    position, at a plurality of what are called reconstruction distances    from said photodetector along said propagation axis; and-   classifying the cell depending on a profile representing a variation    in said characteristic quantity along the propagation axis, this    classification allowing the state of said cell to be determined from    among preset states.

The profile is defined depending on the value of the characteristicquantity and determined at said plurality of distances.

In particular, the preset states may comprise a living state and a deadstate. The method is then able to classify an examined cell anddetermine whether it is dead or alive.

By applying a digital reconstruction algorithm, what is meant is theapplication of a propagation operator to an image, generally in the formof a convolution product.

Each characteristic quantity is in particular obtained by estimating, atsaid reconstruction distance, a complex expression of the light wave towhich the matrix-array photodetector is exposed. The characteristicquantity may be obtained from the modulus or argument of said complexexpression.

The classification may be carried out by comparing said variation insaid characteristic quantity to preset reference profiles.

According to one embodiment, the method includes:

-   determining a complex image called the reference complex image by    applying a digital reconstruction algorithm to the image acquired by    the matrix-array photodetector;-   on the basis of said reference complex image, estimating at least    one characteristic quantity of the light wave to which the    matrix-array photodetector is exposed, at a plurality of    reconstruction distances from the latter.

The method may then include:

-   applying a propagation operator to the reference complex image, so    as to calculate what are called secondary complex images for a    plurality of distances from the reconstruction plane or from the    plane in which the matrix-array photodetector lies; and-   determining a characteristic quantity at each of said distances,    from each secondary complex image.

The reference complex image may be a complex image formed in areconstruction plane that is away from the plane of the sample. It mayalso be a question of a complex image formed in the detection plane.

The method may comprise a step of reconstructing an image of saidcharacteristic quantity in a plane parallel to the detection plane, andat said reconstruction distance, the value of said characteristicquantity at said position of the cell, and at said reconstructiondistance, being determined depending on this image.

The position of each cell, in a plane parallel to the detection plane,may be determined using the image acquired by the matrix-arrayphotodetector or using a reconstructed image such as described in thepreceding paragraph.

The light source may be a spatially coherent source. It may inparticular be a question of a light-emitting diode. The light source mayalso be temporally coherent; it may in particular be a question of alaser diode.

The matrix-array photodetector or image sensor includes a matrix arrayof pixels that are able to collect the light wave to which thephotodetector is exposed. The distance between the pixels and the samplemay vary between 50 μm and 2 cm, and preferably between 100 μm and 5 mm.Preferably the sample is not placed in direct contact with the pixels ofthe matrix-array photodetector.

Preferably, no magnifying optics are placed between the sample and thematrix-array photodetector.

Another subject of the invention is a device for discriminating a livingcell from a dead cell, said cell being placed in a sample, the devicecomprising:

-   a light source that is arranged to produce an incident light wave,    along a propagation axis, in the direction of said sample;-   a matrix-array photodetector arranged to acquire an image of the    sample, on being exposed to a light wave resulting from interference    between said incident light wave and a diffraction wave formed by    said cell;-   a holder, for holding the sample between said light source and the    matrix-array photodetector;    the device being characterized in that it includes a processor    configured to implement the following steps:-   determining a position of said cell in a plane parallel to a    detection plane in which the matrix-array photodetector lies;-   applying a digital reconstruction algorithm to said acquired image,    so as to determine at least one characteristic quantity of the light    wave to which the matrix-array photodetector is exposed, at said    position, at a plurality of what are called reconstruction distances    from said photodetector along the propagation axis; and-   classifying said cell depending on a profile representing the    variation in said characteristic quantity along the propagation    axis, this classification being suitable for determining the state    of the cell from among preset states.    The processor may be a microprocessor, connected to a programmable    memory, including a sequence of instructions for carrying out steps    described in this description.

Preferably, the device includes no magnifying optics between thephotodetector and the analyzed sample.

The sample may be placed in a transparent chamber, placed between thephotodetector and the light source.

Another subject of the invention is an incubator, intended for thegrowth of cells, comprising a device such as described above.

FIGURES

FIG. 1 shows the device according to one embodiment of the invention.

FIG. 2 shows an image acquired by the photodetector in a first exampleembodiment.

FIGS. 3A to 3C show, for a first example embodiment, images of the phaseof the light wave incident on the detector, these images being issuedfrom a holographic reconstruction at three different reconstructiondistances.

FIGS. 4A and 4B respectively show, for a first example embodiment, theprofile of the phase and the profile of another characteristic quantity,called the complementary amplitude, along the propagation axis, for 5cells.

FIGS. 5A and 5B respectively show, for a second example embodiment, theprofile of the phase and the profile of another characteristic quantity,called the complementary amplitude, along the propagation axis, for aplurality of cells.

FIGS. 6A and 6B respectively show, for a third example embodiment, theprofile of the phase and the profile of another characteristic quantity,called the complementary amplitude, along the propagation axis, for aplurality of cells.

FIG. 7 shows, in relation with this third example embodiment, theprofile of a composite quantity combining the phase and absorption alongthe propagation axis for a plurality of cells.

FIG. 8A illustrates the main steps of a method allowing a complex imageof a sample to be calculated in a reconstruction plane.

FIGS. 8B, 8C, 8D, 8E and 8F respectively show:

-   an image acquired by the matrix-array photodetector, this image also    being referred to as a “hologram”;-   an image reconstructed in a reconstruction plane in a first    iteration of the method shown in FIG. 8A;-   an image showing a quantity associated with each pixel of the image    shown in FIG. 8C;-   a representation of an image, called a reference complex image,    reconstructed after a plurality of iterations of the method shown in    FIG. 8A; and-   a profile obtained on the basis of secondary complex images formed    from the reference complex image.

FIG. 9A is a hologram acquired by an image sensor, the sample includingcells dispersed in an aqueous solution. FIGS. 9B and 9C respectivelyshow the modulus and phase of a complex image that is what is called areference image, this complex image being formed in a reconstructionplane. FIGS. 9D and 9E are profiles respectively showing a variation inthe modulus and phase of the light wave to which the image sensor isexposed, along a propagation axis passing through a first cell. FIGS. 9Fand 9G are profiles respectively showing a variation in the modulus andphase of the light wave to which the image sensor is exposed, along apropagation axis passing through a second cell. FIG. 9H is a microscopeimage of the observed sample.

DISCLOSURE OF PARTICULAR EMBODIMENTS

FIG. 1 shows an example of the device that is one subject of theinvention. A light source 11 is able to produce a light wave 12, calledthe incident light wave, in the direction of a sample 14, along apropagation axis Z. The sample 14 includes a culture medium 6 and cells1, 2, 3, 4, 5 the state of which it is desired to determine—it is inparticular desired to determine whether they are alive or dead.

The distance Δ between the light source and the sample is preferablylarger than 1 cm. It is preferably comprised between 2 and 10 cm and istypically 5 cm. Preferably, the light source, seen by the sample, may beconsidered to be point-like. This means that its diameter (or itsdiagonal) must be smaller than one fifth and better still one tenth ofthe distance between the sample and the light source. Thus, the lightreaches the sample in the form of plane waves, or waves that may beconsidered as such.

The light source 11 may be a point source, or be associated with adiaphragm (not shown in FIG. 1) so as to appear point-like. The apertureof the diaphragm is typically comprised between 50 μm and 1 mm andpreferably between 50 μm and 500 μm.

The diaphragm may be replaced by an optical fiber, a first end of whichis placed facing a light source, and a second end of which is placedfacing the sample. In this case, said second end may be likened to apoint light source 11.

The sample 14 is bounded by a chamber, including a base 15 and a cover13. The side walls of the chamber have not been shown. Typically achamber is a petri dish or a well of a multi-well plate. In the exampleconsidered here, the bottom 15 and the cover 13 consist of 2 transparentslides that are a distance of 100 μm apart. The distance d between thecells 1,2,3,4,5 and the photodetector 16 is equal to 3450 μm.

Generally, the thickness of the chamber, along the propagation axis Z,is preferably smaller than a few cm, for example smaller than 5 cm, oreven smaller than 1 cm.

The light source 11 may be temporally coherent but this is notnecessary.

In this example, the light source is an OSRAM light-emitting diode, ofreference LA E67B-U2AA-24-1. It is located a distance Δ equal to 5 cmfrom the sample.

The sample 14 is placed between the light source 11 and a matrix-arrayphotodetector 16. The latter preferably lies in a detection plane Ppreferably lying parallelly, or substantially parallelly, to the base 15of the chamber bounding the sample. The detection plane P preferablylies perpendicularly to the propagation axis Z.

The expression substantially parallelly means that the two elements maynot be rigorously parallel, an angular tolerance of a few degrees,smaller than 10°, being acceptable.

Preferably, the light source is of small spectral width, for example ofspectral width smaller than 200 nm or even 100 nm or indeed 25 nm. Theexpression spectral width designates the full width at half maximum ofthe emission peak of the light source.

The photodetector 16 may be a matrix-array photodetector including amatrix-array of CCD or CMOS pixels. CMOS photodetectors are preferredbecause the size of the pixels is smaller, this allowing images thespatial resolution of which is more favorable to be acquired. In thisexample, the detector is a 12-bit APTINA sensor of reference MT9P031. Itis a question of an RGB CMOS sensor the inter-pixel pitch of which is2.2 μm. The useful area of the photodetector is 5.7×4.3 mm².Photodetectors the inter-pixel pitch of which is smaller than 3 μm arepreferred, because they allow images with a satisfactory spatialresolution to be obtained.

Preferably, the photodetector comprises a matrix-array of pixels, abovewhich array a transparent protective window is placed. The distancebetween the matrix-array of pixels and the protective window isgenerally comprised between a few tens of μm to 150 or 200 μm.

Generally, and whatever the embodiment, the distance d between aparticle and the pixels of the photodetector is preferably comprisedbetween 50 μm and 2 cm and preferably comprised between 100 μm and 2 mm.

The absence of magnifying optics between the matrix-array photodetector16 and the sample 14 will be noted. This does not prevent focusingmicro-lenses optionally being present level with each pixel of thephotodetector 16.

In this first example, the culture medium is a Dulbecco's ModifiedEagle's Medium (DMEM). The sample also contains fibroblast 3T3 cells,the concentration of which is about 0.5×10⁶ cells per ml.

FIG. 2 shows an image obtained by the photodetector 16. This figureshows an overall diffraction pattern, in which elementary diffractionpatterns 31, 32, 33, 34, 35, each elementary diffraction pattern beingassociated with respective cells 1, 2, 3, 4 and 5, may be seen. Eachelementary diffraction pattern comprises a central disc-shaped zone,around which alternately dark and light concentric rings extend. Thezone referenced by the number 6 corresponds to a background zoneincluding no cell.

Each elementary diffraction pattern (31, . . . 35) is formed by theinterference between the incident light wave 12 produced by the source11, upstream of the sample, and a diffraction wave produced bydiffraction of this incident wave by each cell (1, . . . ,5). Thus, thephotodetector 16 is exposed to a light wave 22 formed by thesuperposition:

-   of the incident light wave 12 emitted by the source 11, upstream of    the sample 14; and-   the diffraction wave produced by each of the cells 1, . . . ,5 or    other diffracting elements present in the sample.

A processor 20 receives the images from the matrix-array photodetector16 and reconstructs characteristic quantities of the light wave 22 towhich the photodetector is exposed, along the propagation axis Z. Thereconstruction is in particular carried out between the photodetectorand the observed sample. The processor 20 may be able to execute asequence of instructions stored in a memory, in order to implement stepsof the identifying method. The microprocessor 20 is connected to amemory 23 able to store instructions for implementing calculating stepsdescribed in this application. It may be linked to a screen 25. Theprocessor may be a microprocessor, or any other electronic computer ableto process the images delivered by the matrix-array photodetector, inorder to execute one or more steps described in this description.

The image shown in FIG. 2 corresponds to the intensity distributionI(x,y), x and y being coordinates in the detection plane P describedabove.

According to well-known digital holographic reconstruction principles,which are described in the publication by Ryle et al, “Digital in-lineholography of biological specimens”, Proc. Of SPIE Vol. 6311 (2006), itis possible to reconstruct a complex expression U(x,y,z) for the lightwave 22 at any point of spatial coordinates (x,y,z), and in particularin a plane located a distance |z| from the photodetector, and parallelto the plane P in which the photodetector lies, by determining theconvolution product of the intensity I(x,y) measured by thephotodetector and a propagation operator h(x,y,z).

The function of the propagation operator h(x,y,z) is to describe thepropagation of the light between the photodetector 16 and a point ofcoordinates (x,y,z). It is then possible to determine the amplitudeu(x,y,z) and the phase φ (x,y,z) of this light wave 22 at this distance|z|, which is called the reconstruction distance, where:

u(x,y,z)=abs [U(x,y,z)]

φ(x,y,z)=arg [U(x,y,z)]

The operators abs and arg return the modulus and argument, respectively.

Application of the propagation operator in particular allows the complexexpression U(x,y,z) to be estimated at a distance |z| from thephotodetector, upstream of the latter. The complex value of the lightwave 22 before the latter reaches the detector is thus reconstructed.Back-propagation is then spoken of. If the coordinate z=0 is attributedto the detection plane P, this back-propagation is implemented byapplying a propagation operator h(x,y,−|z|).

The terms upstream and downstream are to be understood with respect tothe propagation direction of the incident wave 12.

If I(x,y)=I(x,y,z=0) corresponds to the intensity of the signal measuredby the photodetector, the relationship between the measured intensityI(x,y) and the complex expression U(x,y) of the light wave, in thedetection plane P, is given by: I(x, y)=|U(x, y)|².

The complex expression of the light wave (22), at a coordinate (x,y,z)is given by

U(x, y, z)=√{square root over (I(x, y))}*h(x, y, z),

the symbol * representing a convolution operator, where:

-   z<0 in the half-space delineated by the detection plane P and    comprising the sample 14; and-   z>0 in the half-space delineated by the detection plane P and not    comprising the sample 14.

In the half-space delineated by the detection plane P and comprising thesample 14, the complex expression of the light wave may also be written:

U(x, y, z)=√{square root over (I(x, y))}*h(x, y, −|z|)

Preferably mathematical preprocessing is applied beforehand to themeasured intensity I(x,y), before the holographic reconstruction. Thisallows the quality of the results to be improved, in particular bydecreasing the number of artefacts created when the propagation operatoris applied.

Thus, an intensity Ī(x, y), called the normalized intensity, isdetermined, such that

Ī(x, y)=(I(x, y)−Average (I))/Average(I)

where

-   I(x,y)=intensity measured by the photodetector at the coordinate    (x,y);-   Average (I)=average of the intensity measured in a region of    interest of the image I, including said coordinate (x,y). This    region of interest may correspond to the entire image formed by the    photodetector.

This pre-processing is equivalent to a normalization of the measuredintensity by the intensity of the incident light wave 12 the latterbeing estimated by the quantity Average (I). It allows artefactsgenerated by the reconstruction process to be limited.

The digital reconstruction may in particular be based on the Fresneldiffraction model. In this example, the propagation operator is theFresnel-Helmholtz function, such that:

${h\left( {x,y,z} \right)} = {\frac{1}{j\; \lambda \; z}e^{j\; 2\; \pi \frac{z}{\lambda}}{{\exp \left( {j\; \pi \frac{x^{2} + y^{2}}{\lambda \; z}} \right)}.}}$

where λ is the wavelength.

Thus,

${U\left( {x,y,z} \right)} = {\frac{1}{j\; \lambda \; z}e^{j\; 2\; \pi \frac{z}{\lambda}}{\int{\int{\sqrt{\overset{\_}{I}\left( {x^{\prime},y^{\prime}} \right)}{\exp \left( {j\; \pi \frac{\left( {x - x^{\prime}} \right)^{2} + \left( {y - y^{\prime \; 2}} \right)}{\lambda \; z}} \right)}{dx}^{\prime}{dy}^{\prime}}}}}$

where

-   x′ and y′ are the coordinates in the plane of the photodetector;-   x and y are the coordinates in the reconstruction plane, the latter    being located at a distance |z| from the photodetector;-   z is the coordinate of the reconstructed image along the propagation    axis Z of the incident light wave 12.

From values of the complex expression U(x,y,z), it is possible toextract characteristic quantities of the light wave 22 resulting fromthe diffraction, by the particles (1,2 . . . 9), of the incident lightwave 12 emitted by the source 11. As mentioned above, it is possible toevaluate the amplitude u(x,y,z) or the phase φ(x,y,z), but it is alsopossible to evaluate any function of the amplitude or phase.

It is for example possible to evaluate a characteristic quantity that iscalled the complementary amplitude ũ(x, y, z) such that:

ũ(x, y, z)=abs(1−U(x, y, z))

From each reconstructed complex expression U(x,y,z), it is possible toform:

-   an image u_(z) of the amplitude of the wave 22, in a plane parallel    to the plane of the detector, at a distance |z| from the latter,    where u_(z)(x,y)=abs [U(x,y,z)];-   an image φ_(z) of the phase of the wave 22, in a plane parallel to    the plane of the detector, at a distance |z| from the latter, where    φ_(z)(x,y)=arg [U(x,y,z)];-   an image    of the complementary amplitude, such as described above, of the wave    22, in a plane parallel to the plane of the detector, at a distance    |z| from the latter, where    (x, y, z)=abs [1−U(x,y,z)].

FIGS. 3A to 3C respectively show images φ_(z) of the phase reconstructedin planes parallel to the matrix-array photodetector with |z|=3050 μm,|z|=3450 μm (z=d) and |z|=3850 μm, respectively, the cells being locatedin the plane |z|=3450 μm.

In each reconstructed image φ_(z) an elementary diffraction pattern (31,32, 33, 34, 35) corresponding to each cell (1,2,3,4,5) of the sample maybe seen, the central portion of each pattern allowing the respectivecoordinates (x₁, y₁), (x₂, y₂), (x₃, y₃), (x₄, y₄) and (x₅, y₅) of cells1 to 5 in the detection plane P to be determined. The value of the phaseφ(x₁y₁,z), φ(x₂, y₂,z), φ(x₃, y₃,z), φ(x₄, y₄,z), φ(x₅, y₅,z) at thevarious values Z in question is determined:

-   at |z|=3850 μm, the phase associated with each cell is positive, and    of value close to π/5;-   at |z|=3450 μm (z=d), the phase associated with cells 1, 2 and 3 is    negative (neighboring−π/5), whereas the phase associated with cells    4 and 5 is positive (neighboring+π/5);-   at |z|=3050 μm, the phase associated with each cell is negative, and    of value close to −π/5.

Thus, in the plane |z|=3450 μm, corresponding to the plane in which thecells are actually located (z=d), the phase of the reconstructed lightwave 22 passing through cells 1, 2 and 3, respectively, is negative,whereas the phase of the reconstructed light wave 22 passing throughcells 4 and 5, respectively, is negative.

Moreover, following these reconstructions, the cells were treated withTrypan blue, then observed using a microscope at a 10× magnification.Trypan blue is a die commonly used in the field of cell viability. Thecells referenced 1, 2 and 3 appeared to be alive, whereas the cellsreferenced 4 and 5 are dyed blue, indicating a dead cell. Theseobservations serve as reference measurement in the analyses detailedbelow.

By reconstructing an image of the radiation to which the detector isexposed in the plane containing the cells (z=3450 μm), and byidentifying, in this reconstructed image, the position of each cell, itis possible to discriminate living cells (negative phase) from deadcells (positive phase).

FIG. 4A illustrates, for each cell n (1≤n≤5), the variation in theprofile φ(x_(n), y_(n),z) of the phase as a function of z, for |z|comprised between 3000 μm and 4000 μm. The profiles corresponding toliving cells (n=1, 2 and 3) are characterized by a marked slope at|z|<3450 μm, whereas the profiles corresponding to the dead cells (n=4or 5) are characterized by a gradual decrease in the phase along thepropagation axis Z, in the direction pointing from the matrix-arrayphotodetector to the sample.

Thus, it is possible to establish a profile representing the variationin the phase of the wave 22 to which the detector is exposed along anaxis, parallel to the propagation axis Z, passing through each cell.This profile may then be used to perform a classification between aliving cell and a dead cell. This profile may in particular be comparedto a library of profiles produced with “standard” cells the state ofwhich is known. In other words, the profile representing the variationin the phase along the propagation axis of the light wave forms asignature of the state of the cell.

Reconstructing a characteristic quantity of the wave 22 resulting fromdiffraction by a particle and the incident wave 12 not at a singlereconstruction distance, but along the propagation axis of the incidentwave, at a plurality of reconstruction distances, allows richerinformation to be obtained. This allows the various states of a cell tobe reliably classified. Moreover, this makes it possible to avoidneeding to know the precise distance separating a cell to becharacterized from the photodetector.

Another indicator may be the distance |z₀| at which the phase valueφ(x_(n), y_(n),z) passes through zero, a cell being considered to bealive if |z₀| is lower than the distance d actually separating the cellfrom the photodetector (in the present case d=3450 μm), and dead in thecontrary case.

FIG. 4B shows, for each cell n (1≤n≤5), the variation in the profileũ(x_(n), y_(n),z) of the complementary amplitude as a function of z, for|z| comprised between 3000 μm and 4000 μm. The profiles corresponding toliving cells (n=1, 2 and 3) are characterized by a minimum valueũ_(min)≤50, whereas for dead cells the minimum value ũ_(min) of theprofile is higher than 50. In other words, it is possible to define athreshold value ũ_(threshold), comparison of this threshold valueũ_(threshold) with a noteworthy point of the profile, in the presentcase the minimum value, allowing the cell to be classed as alive ordead.

From FIG. 4B it will also be noted that when the cells are alive, theminimum value ũ_(min) of the profile is reached at |z|<3450 μm, this notbeing the case for dead cells. In other words, it is possible toidentify the position z_(min), along the propagation axis Z, of anoteworthy point of the profile, in the present case a minimum, and tocompare this position to the distance d between the analyzed cell andthe photodetector. If |z_(min)|≤d, the cell is considered to be viable.Otherwise, it is considered to be dead.

It is therefore possible to establish a profile representing thevariation in the complementary amplitude ũ of the light wave 22 to whichthe detector is exposed, along the propagation axis Z and passingthrough each cell, and to use this profile to perform a classificationbetween a living cell and a dead cell. This profile may in particular becompared to a library of profiles produced with “standard” cells thestate of which is known. In other words, the profile representing thevariation in the complementary amplitude ũ along the propagation axisforms a signature of the state of the cell.

In a second example, the device is similar to that implemented above.The characterized cells are PC12 cells. Just as in the first exampleabove, an image was acquired on the matrix-array photodetector, in anidentical configuration to the configuration shown in FIG. 1. This imageallowed a complex expression U(x,y,z) of the wave 22 to which thephotodetector was exposed to be reconstructed, along the propagationaxis Z, the reconstruction distance varying from 3000 μm to 3800 μm.

A reference measurement was then carried out, using staining with Trypanblue, allowing dead cells D and living cells A to be identified.

FIG. 5A shows the variation in the phase φ(x_(n), y_(n),z) as a functionof |z|, (x_(n),y_(n)) being the coordinates of the center of eachexamined cell n. Just as in the preceding example, it is observed that:

-   the phase φ(x_(n), y_(n), |z|=d=3450 μm) is negative for living    cells, and positive or zero for dead cells;-   the profile φ(x_(n), y_(n),z) associated with each living cell is    characterized by a marked decrease in the phase at |z|<d, whereas    the profile φ(x_(n), y_(n),z) associated with each dead cell is    characterized by a slower variation in the profile as a function    of z. The profile representing the variation in the phase along the    propagation axis Z therefore forms a signature of the state of the    cell; and-   the value |z₀| at which the phase of the reconstructed wave 22 is    equal to 0 varies depending on the state of the cells: |z₀|<d for    living cells and |z₀|≤d for dead cells.

Thus there are 3 criteria for classifying a cell: value of the phase at|z|=d, variation in the phase as a function of z and the value |z₀| atwhich the value of the phase of the complex expression of thereconstructed wave 22 is zero.

FIG. 5B shows the variation in the complementary amplitude ũ (x_(n),y_(n), z) such as defined above as a function of z, (x_(n),y_(n)) beingthe coordinates of the center of each examined cell n. Just as in thepreceding example, the variation in the profile of the complementaryamplitude is different depending on whether the cell is alive or dead.In particular, when the minimum value ũ_(min) of the profile is lowerthan a threshold value ũ_(threshold), here of about 100, a cell isdeclared to be alive, and dead in the contrary case

In a third example, the device is similar to that implemented above. Thecharacterized cells are CHO cells (CHO standing for Chinese hamsterovary—cell line derived from the ovary of the Chinese hamster). Just asin the two examples above, an image is acquired on the matrix-arrayphotodetector, in an identical configuration to the configuration shownin FIG. 1. This image allowed a complex expression U(x,y,z) of the wave22 to which the photodetector is exposed to be reconstructed, along thepropagation axis Z, the reconstruction distance |z| varying from 3000 μmto 3800 μm.

A reference measurement was then carried out, using staining with Trypanblue, allowing dead cells D and living cells A to be identified.

FIG. 6A shows the variation in the phase φ(x_(n), y_(n),z) as a functionof z, (x_(n),y_(n)) being the coordinates of the center of eachcharacterized cell n. Just as in the preceding example, it is observedthat:

-   the phase φ(x_(n), y_(n), |z|=d=3450 μm) is negative for living    cells, and positive for dead cells;-   the profile φ(x_(n), y_(n),z) associated with each living cell is    characterized by a marked decrease in the phase at |z|<d, whereas    the profile φ(x_(n), y_(n),z) associated with each dead cell is    characterized by a slower variation in the profile as a function    of z. The profile representing the variation in the phase along the    propagation axis Z therefore forms a signature of the state of the    cell; and-   the value |z₀| at which the phase of the wave 22 is equal to 0    varies depending on the state of the cells: |z₀|<d for living cells    and |z₀|>d for dead cells.

FIG. 6B shows the variation in the complementary amplitude ũ (x_(n),y_(n), z) such as defined above as a function of z, (x_(n),y_(n)) beingthe coordinates of the center of each examined cell n. Just as in thepreceding example, the variation in the profile of the complementaryamplitude is different depending on whether the cell is alive or dead.In particular, when the minimum value ũ_(min) of the profile is lowerthan a threshold value ũ_(threshold), here equal to 30, a cell isdeclared to be alive, or dead in the contrary case.

According to one variant, the classification between a living cell and adead cell is achieved by combining, for a given height z, variousparameters of the light radiation 22 to which the detector is exposed.According to one example, the phase φ(x,y,z) and the complementaryamplitude ũ (x,y,z) are determined along the propagation axis Z, theclassification being achieved using the ratio of these two parameters.

FIG. 7 shows the profile, along the propagation axis Z, of the compositequantity k(x,y,z) such that

${{k\left( {x,y,z} \right)} = {\frac{\phi \left( {x,y,z} \right)}{\overset{\sim}{u}\left( {x,y,z} \right)} - {k\left( {x_{6},y_{6},z} \right)}}},$

the term k(x₆, y₆, z) representing the ratio

$\frac{\phi \left( {x,y,z} \right)}{\overset{\sim}{u}\left( {x,y,z} \right)}$

determined in a portion 6 of the sample exempt of cells. This ratio maybe called the reference ratio.

This figure shows the variation in the composite quantityk(x_(n),y_(n),z) for n cells, each cell n being identified by itsposition in the plane (x_(n),y_(n)) of the photodetector.

The value of the composite quantity, at a given reconstruction distancez, is systematically higher for living cells than for dead cells. It isthus possible to define a threshold k_(threshold)(z), such that ifk(x_(n),y_(n), z)≥k_(threshold)(z), the cell centered on the position(x_(n),y_(n)), in the plane P, is alive, or dead in the contrary case.

Application of a digital propagation operator h to an image I, orhologram, acquired by a matrix-array photodetector 16 may have certainlimits, because the acquired image includes no phase-relatedinformation. Thus, before the profile is established, it is preferableto obtain information relating to the phase of the light wave 22 towhich the photodetector 16 is exposed. This phase-related informationmay be obtained by reconstructing a complex image U_(z) of the sample14, using methods described in the prior art, so as to obtain anestimation of the amplitude and phase of the light wave 22 in the planeP of the matrix-array photodetector 16 or in a reconstruction planeP_(z) located at a distance |z| from the latter. The inventors havedeveloped a method based on the calculation of a reference compleximage, which method is described with reference to FIG. 8A. This methodcomprises the following steps:

-   Acquiring an image I of the sample 14 with the matrix-array    photodetector 16, this image forming the hologram (step 100).-   Calculating a complex image called the reference image U_(ref) of    the sample 14 in a reconstruction plane P_(z) or in the detection    plane P, this reference complex image including information on the    phase and amplitude of the light wave 22 to which the matrix-array    photodetector 16 is exposed; this step is carried out by applying    the propagation operator h described above to the acquired image I    (steps 110 to 170). This complex image is said to be a reference    image because the formation of the profile on the basis of which the    particle is characterized is based thereon.-   Selecting a radial position (x, y) of a particle in the detection    plane or in a plane parallel to the latter (step 180), either using    the reference complex image U_(ref), or the image I acquired by the    photodetector 16.-   Applying the propagation operator it to the reference complex image    U_(ref) so as to calculate complex images U_(ref,z′) called    secondary images, along the propagation axis Z (step 185).-   On the basis of each secondary complex image U_(ref,z′), estimating    a characteristic quantity of the light wave 22, at the radial    position (x, y) of the particle selected beforehand, and at a    plurality of distances from the reconstruction plane P_(z) (or from    the detection plane P), and then forming a profile representing a    variation in said characteristic quantity along the propagation axis    Z (step 190).-   Characterizing the particle depending on said profile. As indicated    above, this characterization may be achieved by comparing the    obtained profile with standard profiles obtained in a calibrating    phase, using standard samples (step 200).

The algorithm presented in FIG. 8A is detailed below, the resultsobtained in certain steps being illustrated in FIGS. 8B to 8F. Steps 110to 170 are a preferred way of obtaining a reference complex image,denoted U_(ref), this image representing a spatial distribution of thecomplex expression of the wave 22 in a reconstruction plane P_(z). Thoseskilled in the art will understand that other algorithms allow such acomplex image to be reconstructed, it for example also beingenvisionable to use the algorithms mentioned with reference to the priorart.

Step 100: Image Acquisition

In this step, the image sensor 16 acquires an image I of the sample 14,and more precisely of the light wave 22 transmitted by the latter, towhich light wave the image sensor is exposed. Such an image, orhologram, is shown in FIG. 8B.

This image was produced using a sample 10 including Chinese hamsterovary (CHO) cells immersed in a saline buffer, the sample beingcontained in a fluidic chamber of 100 μm thickness placed at a distanced of 1500 μm from a CMOS sensor. The sample was illuminated with alight-emitting diode 11 the spectral emission band of which was centeredon a wavelength of 450 nm and which was located at a distance D=8 cmfrom the sample.

Step 110: Initialization

In this step, an initial image U₀ ^(k=0) of the sample 14 is defined,from the image I acquired by the image sensor 16. This step is aninitialization of the iterative algorithm described below with regard tosteps 120 to 180, the exponent k indicating the rank of each iteration.The modulus u₀ ^(k=0) of the initial image U₀ ^(k=0) may be obtained byapplying the square-root operator to the image I acquired by the imagesensor, in which case u₀ ^(k=0)=√{square root over (I₀)}.

The phase φ₀ ^(k=0) of the initial image U₀ ^(k=0) is either consideredto be zero in each pixel (x, y), or preset to an arbitrary value.Specifically, the initial image U₀ ^(k=0) results directly from theimage I acquired by the matrix-array photodetector 16. However, thelatter includes no information relating to the phase of the light wave22 transmitted by the sample 14, the image sensor 16 being sensitiveonly to the intensity of this light wave.

Step 120: Propagation

In this step, the image U₀ ^(k−1) obtained in the plane of the sample ispropagated to a reconstruction plane P_(z), by applying a propagationoperator such as described above, so as to obtain a complex image U_(z)^(k), representative of the sample 14, in the reconstruction planeP_(z). The propagation is carried out by convoluting the image U₀ ^(k−1)with the propagation operator h_(−z′) such that:

U _(z) ^(k) =U ₀ ^(k−1) *h _(−z′)

the symbol * representing a convolution operator. The index −zrepresents the fact that the propagation is carried out in a directionopposite to that of the propagation axis Z. Back-propagation is spokenof.

In the first iteration (k=1), U₀ ^(k=0) is the initial image determinedin step 110. In the following iterations, U₀ ^(k−1) is the complex imagein the detection plane P updated in the preceding iteration.

The reconstruction plane P_(z) is a plane away from the detection planeP, and preferably parallel to the latter. Preferably, the reconstructionplane P_(z) is a plane P₁₄ in which the sample 14 lies. Specifically, animage reconstructed in this plane allows a generally high spatialresolution to be obtained. It may also be a question of another plane,located a nonzero distance from the detection plane, and preferablyparallel to the latter, for example a plane lying between thematrix-array photodetector 16 and the sample 14.

FIG. 8C shows the modulus of an image U_(z) ^(k=1) reconstructed at adistance of 1440 μm from the detection plane P by applying thepropagation operator defined above to the hologram of FIG. 8B. Thisimage is the complex image, in the reconstruction plane, established inthe first iteration.

Step 130: Calculation of an Indicator in a Plurality of Pixels

In this step, a quantity ε^(k)(x, y) associated with each pixel of aplurality of pixels (x, y) of the complex image U_(z) ^(k) iscalculated, preferably in each of these pixels. This quantity depends onthe value U_(z) ^(k)(x, y) of the image U_(z) ^(k), or of its modulus,in the pixel (x, y) for which it is calculated. It may also depend on adimensional derivative of the image in this pixel, for example themodulus of a dimensional derivative of this image.

In this example, the quantity associated with each pixel (x, y) is basedon the modulus of a dimensional derivative, such that:

$\begin{matrix}{{ɛ^{k}\left( {x,y} \right)} = {\sqrt{{\frac{\partial{U_{z}^{k}\left( {x,y} \right)}}{\partial x}}^{2} + {\frac{\partial{U_{z}^{k}\left( {x,y} \right)}}{\partial y}}^{2}}.}} & \;\end{matrix}$

Since the image is discretized into pixels, the derivative operators maybe replaced by Sobel operators, such that:

${ɛ^{k}\left( {x,y} \right)} = \sqrt{{\left( {S_{x}*{U_{z}^{k}\left( {x,y} \right)}} \right)\; \left( {S_{x}*{U_{z}^{k}\left( {x,y} \right)}} \right)^{*}} + {\left( {S_{y}*{U_{z}^{k}\left( {x,y} \right)}} \right)\; \left( {S_{y}*{U_{z}^{k\;}\left( {x,y} \right)}} \right)^{*}}}$

where:

-   ( ) * is the complex conjugate operator; and

S_(x) and S_(y) are Sobel operators along two orthogonal axes X and Y ofthe reconstruction plane P_(z).

In this example,

$S_{x} = \begin{bmatrix}1 & 0 & {- 1} \\2 & 0 & {- 2} \\1 & 0 & {- 1}\end{bmatrix}$

and S_(y) is the transposed matrix of S_(x).

FIG. 8D shows, in the form of an image, the value of the modulusε^(k)(x, y) in each pixel of the image A_(z) ^(k=1) shown in FIG. 8C.

Step 140: Establishment of a Noise Indicator Associated with the ImageU_(z) ^(k)

In step 130, quantities ε^(k)(x, y) were calculated in a plurality ofpixels of the complex image U_(z) ^(k). These quantities may form avector E^(k), the terms of which are the quantities ε^(k)(x, y)associated with each pixel (x, y). In this step, an indicator, calledthe noise indicator, is calculated from a norm of the vector E^(k).Generally, an order is associated with a norm, such that the norm∥x∥_(p) of order p of a vector x of dimension n of coordinates (x_(1,)x_(2,) . . . x_(n,)) is such that: ∥x∥_(p)=(Σ_(i=1)^(n)|x_(i)|^(p))^(1/p), where p≥0.

In the present case, a norm of order 1 is used, in other words p=1.Specifically, the inventors have estimated that a norm of order 1, or oforder lower than or equal to 1, is particularly suitable for such asample, as explained below.

In this step, the quantity ε^(k)(x, y) calculated from the complex imageU_(z) ^(k), in each pixel (x, y) of the latter, is summed so as to forma noise indicator ε^(k) associated with the complex image U_(z) ^(k).

Thus,

ε^(k)=Σ_((x,y))ε^(k)(x, y)

This noise indicator ε^(k) corresponds to a norm of the total variationin the complex image A_(z) ^(k).

With reference to the example of FIG. 8D, the noise indicator ε^(k=1) isobtained, in the first iteration, by summing the value of the pixels ofthis image.

Because a norm of order 1, or of order lower than or equal to 1, isused, the value of the noise indicator ε^(k) decreases as the compleximage U_(z) ^(k) becomes more and more representative of the sample.Specifically, in the first iterations, the value of the phase φ₀ ^(k)(x,y), in each pixel (x, y) of the image U₀ ^(k) is poorly estimated.Propagation of the image of the sample from the detection plane P to thereconstruction plane P_(z) is then accompanied by substantialreconstruction noise, as mentioned with regard to the prior art. Thisreconstruction noise takes the form of fluctuations in the reconstructedimage. Because of these fluctuations, a noise indicator ε^(k), such asdefined above, increases in value as the contribution of thereconstruction noise, in the reconstructed image, increases.Specifically, the fluctuations due to the reconstruction noise tend toincrease the value of this indicator.

An important aspect of this step consists in determining, in thedetection plane P, phase values φ₀ ^(k)(x, y) for each pixel of theimage of the sample U₀ ^(k), this allowing, in a following iteration, areconstructed image U_(z) ^(k+1) to be obtained the indicator of whichε^(k+1) is lower than the indicator ε^(k).

In the first iteration, as explained above, relevant information isavailable only on the intensity of the light wave 22 and not on itsphase. The first image U_(Z) ^(k=1) reconstructed in the reconstructionplane P_(z) is therefore affected by a substantial amount ofreconstruction noise, because of the absence of relevant information asto the phase of the light wave 22 in the detection plane P. Therefore,the indicator ε^(k=1) is high. In following iterations, the algorithmcarries out a gradual adjustment of the phase φ₀ ^(k)(x, y) in thedetection plane P, so as to gradually minimize the indicator ε^(k).

The image U₀ ^(k) in the detection plane is representative of the lightwave 22 in the detection plane P, both from the point of view of itsintensity and of its phase. Steps 120 to 160 aim to establish,iteratively, for each pixel of the image U₀ ^(k), the value of the phaseφ₀ ^(k)(x, y) which minimizes the indicator ε^(k), the latter beingobtained from the image U_(z) ^(k) obtained by propagating the image U₀^(k−1) to the reconstruction plane P_(z).

The minimization algorithm may be a gradient descent algorithm, or aconjugated gradient descent algorithm, the latter being described below.

Step 150: Adjustment of the value of the phase in the detection plane.

Step 150 aims to determine a value of the phase φ₀ ^(k)(x, y) of eachpixel of the complex image U₀ ^(k), so as to minimize, in the followingiteration k+1, the indicator ε^(k+1) resulting from a propagation of thecomplex image U₀ ^(k) to the reconstruction plane P_(z). To do this, aphase vector φ₀ ^(k) is established, each term of which is the phase φ₀^(k)(x, y) of a pixel (x, y) of the complex image U₀ ^(k). The dimensionof this vector is (N_(pix), 1), where N_(pix) is the number of pixels inquestion. This vector is updated in each iteration, using the followingupdating expression:

φ₀ ^(k)(x, y)=φ₀ ^(k−1)(x, y)+α^(k) p ^(k)(x, y)

where:

-   α^(k) is an integer, called the “step size”, representing a    distance;-   p^(k) is a direction vector, of dimension (N_(pix), 1), each term    p(x, y) of which forms a direction of the gradient ∇ε^(k) of the    indicator ε^(k).

This equation may be expressed in vectorial form as follows:

φ₀ ^(k)=φ₀ ^(k−1)+α^(k) p ^(k)

It may be shown that:

p ^(k)=−∇ε^(k)+β^(k) p ^(k−1)

where:

∇ε^(k) is a gradient vector, of dimension (N_(pix), 1), each term ofwhich represents a variation in the indicator ε^(k) as a function ofeach of the degrees of freedom of the unknowns of the problem, i.e. theterms of the vector φ₀ ^(k);

-   p^(k−1) is a direction vector established in the preceding    iteration;-   β^(k) is a scale factor applied to the direction vector p^(k−1).

Each term ∇ε^(k)(x, y) of the gradient vector ∇ε is such that

${\nabla{ɛ^{k}\left( r^{\prime} \right)}} = {\frac{\partial ɛ^{k}}{\partial{\phi_{0}^{k}\left( r^{\prime} \right)}} = {- {{Im}\left( {{U_{0}^{k^{*}}\left( r^{\prime} \right)}\left( {\left( {{S_{x}*\frac{S_{x}*U_{z}^{k}}{ɛ^{k}}} + {S_{y}*{\frac{S_{y}*U_{z}^{k}}{ɛ^{k}} \cdot}}} \right)*h_{z}} \right)\left( r^{\prime} \right)} \right)}}}$

where Im is an operator returning the imaginary part of the operand andr′ is a coordinate (x, y) in the detection plane.

The scale factor β^(k) may be expressed such that:

$\beta^{(k)} = \frac{{\nabla ɛ^{(k)}} \cdot {\nabla ɛ^{(k)}}}{{\nabla ɛ^{({k - 1})}} \cdot {\nabla ɛ^{({k - 1})}}}$

The step size α^(k) may vary depending on the iteration, for examplefrom 0.03 in the first iterations to 0.0005 in the last iterations.

The updating equation allows an adjustment of the vector φ₀ ^(k) to beobtained, this leading to an iterative update of the phase φ₀ ^(k)(x, y)in each pixel of the complex image U₀ ^(k). This complex image U₀ ^(k),in the detection plane, is then updated with these new values of thephase associated with each pixel. It will be noted that the modulus ofthe complex image U₀ ^(k) is not modified, the latter being determinedfrom the image acquired by the matrix-array photodetector 16, such thatu₀ ^(k)(x, y)=u₀ ^(k)(x, y).

Step 160: Reiteration of or exit from the algorithm.

Provided that a convergence criterion has not been reached, step 160consists in reiterating the algorithm, with a new iteration of steps 120to 160, on the basis of the complex image U₀ ^(k) updated in step 150.The convergence criterion may be a preset number K of iterations, or aminimum value of the gradient ∇ε^(k) of the indicator, or a differenceconsidered to be negligible between two consecutive phase vectors φ₀^(k−1),φ₀ ^(k). When the convergence criterion is reached, theestimation is considered to be a correct estimation of a complex imageof the sample, in the detection plane P or in the reconstruction planeP.

Step 170: Obtainment of the reference complex image.

At the end of the last iteration, the method may comprise propagatingthe complex image U₀ ^(k) resulting from the last iteration to thereconstruction plane P_(z), so as to obtain a reference complex imageU_(ref)=U_(z) ^(k). Alternatively, the reference complex image U_(ref)is the complex image U₀ ^(k) resulting from the last iteration in thedetection plane P. When the density of the particles is high, thisalternative is however less advantageous because the spatial resolutionin the detection plane P is lower than in the reconstruction planeP_(z), in particular when the reconstruction plane P_(z) corresponds toa plane P₁₄ in which the sample 14 lies.

FIG. 8E shows an image of the modulus u_(z) ^(k=30) of each pixel of thereference complex image U_(Z) ^(k=30) obtained in a reconstruction planeP_(z) after 30 iterations. This image may be compared to FIG. 8C,showing a similar image A_(Z) ^(k=1) obtained in the first iteration. Aclear decrease in reconstruction noise is observed, in particularbetween each pixel. Moreover, the spatial resolution of this imageallows a good identification of the radial coordinates (x, y) of eachparticle.

Step 180: Selection of particle radial coordinates.

In this step, the radial coordinates (x, y) of a particle are selectedfrom the reference image U_(ref)=U_(Z) ^(k=30), for example from theimage of its modulus u_(ref=)u_(Z) ^(k=30) or the image of its phaseφ_(ref=)φ_(Z) ^(k=30). As mentioned above, the expression radialcoordinate designates a coordinate in the detection plane or in thereconstruction plane. It is also envisionable to carry out thisselection on the basis of the hologram I₀ or of the complex image U₀^(k) obtained in the detection plane following the last iteration.However, when the number of particles increases, it is preferable tocarry out this selection on the image formed in the reconstructionplane, because of its better spatial resolution, in particular when thereconstruction plane P_(z) corresponds to the plane of the sample P₁₄.In FIG. 8E, the selection of a particle, which is encircled by a dottedoutline, has been shown.

Step 185: Application of a Propagation Operator

In this step 185, the reference complex image U_(ref) is propagated to aplurality of reconstruction distances, using a propagation operator hsuch as defined above, so as to obtain a plurality of what are calledsecondary complex images U_(ref,z) reconstructed at various distancesfrom the detection plane P or from the reconstruction plane P_(z). Thus,this step comprises determining a plurality of complex images U_(ref,z)such that:

U _(ref,z) =U _(ref) *h _(z) with z _(min) ≤z≤z _(max).

The values z_(min) and z_(max) the minimum and maximum coordinates,along the axis Z, to which the reference complex image is propagated.Preferably, the complex images are reconstructed at a plurality ofcoordinates z between the sample 14 and the image sensor 16. The compleximages may be formed on either side of the sample 14.

These secondary complex images are established by applying a holographicreconstruction operator h to the reference image U_(ref). The latter isa complex image correctly describing the light wave 22 to which theimage sensor is exposed, and in particular its phase, following theiterations of the steps 120 to 160. Therefore, the secondary imagesU_(ref,z) form a good descriptor of the propagation of the light wave 22along the propagation axis Z.

Step 190: Formation of a Profile

In this step, from each secondary complex image U_(ref,z′) acharacteristic quantity, such as defined above, of the light wave 22 isdetermined so as to define a profile representing the variation in saidcharacteristic quantity along the propagation axis Z. The characteristicquantity may, for example, be the modulus or the phase, or a combinationthereof. FIG. 8F shows the variation in the phase φ(z) of the light wave22 along the propagation axis Z.

Step 200: Characterization

The particle may then be characterized from the profile formed in thepreceding step. Preferably, there is available a database of standardprofiles formed in a learning phase using known standard samples. Thecharacterization is then carried out by comparing or classifying theformed profile on the basis of the standard profiles.

This embodiment, which is based on formation of a reference compleximage, was implemented, using the norm of the total variation, on CHO(Chinese hamster ovary) cells immersed in a CD CHO culture medium(Thermo Fisher). The sample was placed in a fluidic chamber of 100 μmthickness and positioned at a distance of 8 cm from a light-emittingdiode, the spectral band of which was centered on 450 nm. The sample wasplaced at a distance of 1500 μm from a CMOS image sensor of 2748×3840pixels. The aperture of the spatial filter 18 had a diameter of 150 μm.

FIG. 9A shows an image I acquired by the matrix-array photodetector 16.The images of the modulus and of the phase of the reference compleximage U_(z) ^(k) reconstructed, in the plane P₁₄ of the sample, areshown in FIGS. 5B and 5C, respectively. These images were obtained in100 iterations. The uniformity of the gray-scale representation of eachcell attests to the quality of the reconstruction. A propagationoperator h such as described above was applied to this reference imagein order to obtain a plurality of secondary complex images U_(ref,z)along the propagation axis Z. Moreover, in the image of the modulus orin the image of the phase of the reference image, two cells wereidentified, respectively encircled by a black dashed outline (cell 10b-1) and a black dotted outline (cell 10 b-2) in FIGS. 9B and 9C. Theradial coordinates (x, y) of these two cells were extracted. For eachcell, a profile u(z) representative of the modulus and a profile φ(z)representative of the phase of the light wave 22 reaching the imagesensor 16 were formed. The value of each point of the profile isobtained by determining the modulus and phase of a respective secondarycomplex image U_(ref,z) at said radial coordinates (x, y).

FIGS. 9D and 9E respectively show the profile of the modulus and of thephase of the cell 10 b-1. FIGS. 9F and 9G respectively show the profileof the modulus and of the phase of the cell 10 b-2.

Moreover, following these reconstructions, the cells were treated withTrypan blue, then observed using a microscope at a 10× magnification.The image obtained is shown in FIG. 9H. The cell 10 b-1 is a livingcell, whereas the cell 10 b-2 appears to be a dead cell.

The profiles of modulus or phase of FIGS. 9D and 9E may be considered tobe representative of a living CHO cell, whereas FIGS. 9F and 9G may beconsidered to be representative of a dead CHO cell. CHO cells may becharacterized on the basis of such profiles.

The examples described above provide simple identification criteriabased on the variation in the profile of a characteristic quantity as afunction of reconstruction distance, and on comparisons using presetthresholds. In addition, other classifying methods that are more complexand more robust may be implemented, without departing from the scope ofthe invention.

1-15. (canceled)
 16. A method for determining a state of a cell, thecell being placed in a sample, the method comprising: illuminating thesample using a light source, the light source producing an incidentlight wave propagating towards the sample along a propagation axis;acquiring, using a matrix-array photodetector, an image of the sample,the sample being placed between the light source and the matrix-arrayphotodetector such that the matrix-array photodetector is exposed to alight wave comprising interference between the incident light wave and adiffraction wave produced by the cell; identifying a position of thecell in a plane parallel to a detection plane in which the matrix-arrayphotodetector lies; applying a digital reconstruction algorithm to theacquired image, to determine at least one characteristic quantity of thelight wave to which the matrix-array photodetector is exposed, at theposition of the cell, at a plurality of reconstruction distances fromthe matrix-array photodetector along the propagation axis; andclassifying the cell depending on a profile representing a variation inthe characteristic quantity as a function of the distance along thepropagation axis, the classification allowing the state of the cell tobe determined from among preset states.
 17. The method of claim 16,wherein the preset states comprise a living cell state and/or a deadcell state.
 18. The method of claim 16, wherein the characteristicquantity is obtained by estimating, at each reconstruction distance, acomplex expression of the light wave to which the matrix-arrayphotodetector is exposed.
 19. The method of claim 18, wherein thecharacteristic quantity is determined from the modulus or the argumentof the complex expression.
 20. The method of claim 16, wherein theclassification is carried out by comparing variation in thecharacteristic quantity to preset reference profiles.
 21. The method ofclaim 16, further comprising reconstructing an image of thecharacteristic quantity in a plane parallel to the detection plane, andat the reconstruction distance, the value of the characteristic quantityat the position of the cell, at the reconstruction distance, beingdetermined depending on this image.
 22. The method of claim 16, whereinthe position of each cell, in a plane parallel to the detection plane,is determined using the image thus reconstructed.
 23. The method ofclaim 16, further comprising: determining a reference complex image, ina reconstruction plane or in the detection plane, by applying a digitalreconstruction algorithm to the image acquired by the matrix-arrayphotodetector; and based on the reference complex image, estimating atleast one characteristic quantity of the light wave to which thematrix-array photodetector is exposed, at a plurality of reconstructiondistances from the matrix-array photodetector.
 24. The method of claim23, further comprising: applying a propagation operator to the referencecomplex image, to calculate secondary complex images for a plurality ofdistances from the reconstruction plane or from the plane in which thematrix-array photodetector lies; and determining a characteristicquantity at each of the reconstruction distances, from each secondarycomplex image.
 25. The method of claim 16, wherein the light source is aspatially coherent source.
 26. The method of claim 16, wherein the lightsource is a light-emitting diode.
 27. The method of claim 16, wherein nomagnifying optics are placed between the sample and the matrix-arrayphotodetector.
 28. A device for determining a state of a cell, the cellbeing placed in a sample, the device comprising: a light sourceconfigured to produce an incident light wave, along a propagation axis,in a direction of the sample; a matrix-array photodetector configured toacquire an image of the sample, on being exposed to a light waveresulting from interference between the incident light wave and adiffraction wave formed by the cell; a holder to hold the sample betweenthe light source and the matrix-array photodetector; a processorconfigured to: identify a position of the cell in a plane parallel to aplane in which the photodetector lies; apply a digital reconstructionalgorithm to the acquired image, to determine at least onecharacteristic quantity of the light wave to which the photodetector isexposed, at the position, at a plurality of reconstruction distancesfrom the photodetector along the propagation axis; and classify the celldepending on a profile representing the variation in the characteristicquantity along the propagation axis, the classification to determine thestate of the cell from among preset states.
 29. The device of claim 28,wherein the device comprises no magnifying optics between thephotodetector and the sample.
 30. An incubator, for growth of cells, theincubator comprising at least one device of claim 28.